| Yes, all other things equal. But it's quite possible for a string with lower tension to have more stiffness than another string with higher tension, if the construction differences (core, winding type) support it. Stiffness equates to the amount of sideways force required to deflect the string, and I will bet that a naked (unwound) string will feel much less stiff than a wound string of equal tension.
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To is a preposition. Much is not a verb.
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